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BITSAT2009MathematicsApplication of DerivativesActual

If (M( )= [ array ccc & - & 0 & & 0 0 & 0 & 1 array ] ); (M( )= [ array ccc & 0 & 0 & 1 & 0 - & 0 & array ] ) then ([M( ) M( )]⁻¹ ) is equal to -

Options

  1. A( M ( ) M ( ) )
  2. B( M (- ) M (- ) )
  3. C( M (- ) M (- ) )
  4. D(- M ( ) M ( ) )

Correct answer

C. ( M (- ) M (- ) )

Step-by-step solution

( aligned & .[ M ( ) M ( )]⁻¹= M ( )⁻¹ M ( )⁻¹ ] & Now~M( )⁻¹ = [ array ccc & & 0 - & & 0 0 & 0 & 1 array ] & = [ array ccc (- ) & - (- ) & 0 (- ) & (- ) & 0 0 & 0 & 1 array ]= M (- ) & M( )⁻¹= [ array ccc & 0 & - 0 & 1 & 0 & 0 & array ] & = [ array ccc (- ) & 0 & (- ) 0 & 1 & 0 - (- ) & 0 & (- ) array ]= M (- ) & [ M ( ) M ( )]⁻¹= M (- ) M (- ) & aligned )

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